Problem: Multiply the following complex numbers: $({-1-i}) \cdot ({-4+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-i}) \cdot ({-4+5i}) = $ $ ({-1} \cdot {-4}) + ({-1} \cdot {5}i) + ({-1}i \cdot {-4}) + ({-1}i \cdot {5}i) $ Then simplify the terms: $ (4) + (-5i) + (4i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-5 + 4)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-5 + 4)i - (-5) $ The result is simplified: $ (4 + 5) + (-1i) = 9-i $